Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations
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Publication:3460208
DOI10.1007/978-3-319-18242-1_7zbMath1456.74018OpenAlexW340879785MaRDI QIDQ3460208
Caterina Ida Zeppieri, Lucia Scardia, Stefan Müller
Publication date: 6 January 2016
Published in: Analysis and Computation of Microstructure in Finite Plasticity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-18242-1_7
Nonlinear elasticity (74B20) Micromechanics of solids (74M25) Homogenization in equilibrium problems of solid mechanics (74Q05)
Related Items (7)
Variational Modeling of Slip: From Crystal Plasticity to Geological Strata ⋮ Homogenization of vector-valued partition problems and dislocation cell structures in the plane ⋮ Line-tension limits for line singularities and application to the mixed-growth case ⋮ Derivation of strain-gradient plasticity from a generalized Peierls-Nabarro model ⋮ Optimal laminates in single-slip elastoplasticity ⋮ Strain-Gradient Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy with Mixed Growth ⋮ Dislocation microstructures and strain-gradient plasticity with one active slip plane
Cites Work
- Unnamed Item
- Currents and dislocations at the continuum scale
- Asymptotic behaviour of a pile-up of infinite walls of edge dislocations
- On a mesoscopic many-body Hamiltonian describing elastic shears and dislocations
- The line-tension approximation as the dilute limit of linear-elastic dislocations
- Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
- Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of \(\mathbf F=\mathbf F^e\mathbf F^p\)
- Gradient theory for plasticity via homogenization of discrete dislocations
- New estimates for elliptic equations and Hodge type systems
- A phenomenological theory for strain gradient effects in plasticity
- Lower bounds for the energy of unit vector fields and applications
- Linearized elasticity as \(\Gamma\)-limit of finite elasticity
- \(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime
- Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity
- Improved lower bounds for Ginzburg-Landau energies via mass displacement
- Plasticity at the micron scale
- Korn's second inequality and geometric rigidity with mixed growth conditions
- Optimal energy scaling for a shear experiment in single-crystal plasticity with cross-hardening
- Existence of minimizers for a polyconvex energy in a crystal with dislocations
- Spontaneous breaking of rotational symmetry with arbitrary defects and a rigidity estimate
- On the analytical and physical foundations of the theory of dislocations and yielding by the differential geometry of continua
- Discrete crystal elasticity and discrete dislocations in crystals
- Relaxation of the single-slip condition in strain-gradient plasticity
- Geometric rigidity for incompatible fields and an application to strain-gradient plasticity
- Line-Tension Model for Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy
- A complete list of invariants for defective crystals
- Variational Approaches and Methods for Dissipative Material Models with Multiple Scales
- Energy Estimates, Relaxation, and Existence for Strain-Gradient Plasticity with Cross-Hardening
- Microstructure in Plasticity, a Comparison between Theory and Experiment
- Lower Bounds for Generalized Ginzburg--Landau Functionals
- Material symmetry and singularities in solids
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous
- Lower semicontinuity and existence of minimizers in incremental finite‐strain elastoplasticity
- Erratum
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